Can 3DView Border Select behavior be changed?
Interesting question, never gave it much though, but now that you mention I did some investigation and came to the conclusion that I find it a smart and consistent system even if apparently unexpected at first.

If you border select only one corner, imagining you are in vertex selection mode, you are technically selecting one vertex only; so Blender automatically extends the selection to all the concurrent edges.



If you fully encapsulate an arbitrary number of edge then Blender will assume you want to select them and ignore the "vertex-extension" mode.



If no vertex is selected and no edge is fully encaspulated then "crossing-mode" is used instead, and any touched edge is selected regardless of being fully inside the border or not.